Roberta wrote:"This" refers to dismissing House. (I saw the program, but I don't remember this scene.)
I understand it this way now:
...
Vogler: Dr. Cuddy, you realize this is going to happen. = You comprehend the fact of dismissing House is going to happen. (But you're behaving unreasonably.)
Cuddy: I can't do it. = I can't vote yes to dismiss him.
Vogler: You can't abstain.
....
Thank you Roberta, very much, for this help.